Why do curved flows accelerate? So I’m a bit of a fluid dynamics nerd, but for a while now this has been bothering me. We know that wings produce lift in part because of the flow accelerating over the top of the curved wing, and as a result of conservation of mass and energy Bernoulli showed that this results in a drop in static pressure. But why does the flow accelerate around a curved shape? I have some vague feeling it is related to circulation around the wing (Γ) but I really can’t work it out; anyone know?
 A: Maybe it would help to understand the flow around a flat plate, where the velocity of the flow is directed normal to the plate.
In the potential flow model, the fluid wraps around the plate. Why does it want to accelerate around the corners?

In reality, there is a wake behind the plate because the flow loses some energy to friction.

Why does the flow want to wrap around and occupy that space? Because there is nothing there and the fluid has pressure.

Imagine the black blob as a vacuum. Taking out a fluid blob near the vacuum, we see that there are no neighboring fluid particles towards the vacuum to supply a pressure. Thus, the pressure imbalance drives the fluid particles towards the vacuum.
To understand your wing example, now try tilting the plate and then adding some curvature.
A: Lets start with knowing that the fluid close to the airfoil surface will follow the contour of the airfoil, otherwise fluid would either penetrate the surface or produce a vacuum.
Based on that premise alone it is possible to infer what kinds of pressure gradients we might expect to see, and then make a guess at the nature of the velocity field.
Because the fluid follows curved paths around the airfoil, it is experiencing accelerations in various directions as it passes the airfoil. These accelerations are aligned with pressure gradients in the fluid.
In this example image the upper streamline is strongly curved near regions 2 and 3, the red arrows show the direction fluid elements must accelerate in order to follow those curves.

Knowing that fluids accelerate away from regions of higher pressure towards regions of lower pressure, we can guess that the area just below the leading edge of the airfoil is a region of higher pressure, and the area just above and behind the leading edge is a region of lower pressure.
Now that we have established which areas are expected to be above and below ambient pressure based on streamline curvature, we can infer how the fluid velocity will change along the surface of the airfoil.
Between regions $1 \rightarrow 2$ the pressure is increasing, and the velocity is decreasing as the fluid increases in pressure.
Between regions $2 \rightarrow 3$ the pressure is decreasing, the velocity is therefore increasing as the fluid accelerates from a high pressure region into a low pressure region.
The fluid then gradually slows down through regions $3 \rightarrow 4 \rightarrow 5$ as it approaches the trailing edge where we expect to find a weak high pressure region.
The fluid weakly accelerates between regions $5 \rightarrow 6$, as it recovers to ambient pressure after leaving the trailing edge.
Now let's look at the pressure field calculated with potential flow. Ambient pressure is marked green, high pressure yellow, and low pressure blue and violet.

Not a bad guess, let's take a look at the velocity field below just to be sure.
Here low velocities are violet, medium velocities blue, and high velocities green and yellow.

Now we see just what we expected to see, an airfoil where fluid moves faster over the upper surface than under the lower surface.
This doesn't just apply to airfoils, any region of curved flow is accompanied by a pressure gradient, and any pressure gradient that is not perfectly parallel with the flow will be accompanied by flow curvature.
